The present invention is generally related to separating individual source signals from a mixture of source signals, and more specifically related to blind source separation.
A classic problem in signal processing, often referred to as blind source separation (“BSS”), involves recovering individual source signals from a composite signal comprising a mixture of those individual signals. An example is the familiar “cocktail party” effect, wherein a person at a party is able to separate a single voice from the combination of all voices in the room. The separation is referred to as “blind” because it is often performed with limited information about the signals and the sources of the signals.
Blind source separation is particularly applicable to cellular and personal wireless communications technologies, wherein many frequency bands have become cluttered with numerous electromagnetic emitters, often co-existing in the same spectrum. The problem of co-channel emitters is expected to only worsen in years to come with the development of low power, unlicensed wireless technologies such as Bluetooth® and other personal area networks. These developments have resulted in the use of multiple sensors and array signal processing techniques to perform spectral monitoring. Such techniques enable the exploitation of spatial information to separate co-channel emitters for detection, classification, and identification. Additionally, many signals designed for a low probability of detection (LPD) or low probability of intercept (LPI) may use ambient background electromagnetic radiation and known co-channel emitters as a means of concealment. Constructing single sensor receiver systems with the required sensitivity to such emitters is generally prohibitive. Thus, many applications utilize BSS and sensor arrays.
As described in “Blind Source Separation Utilizing A Spatial Fourth Order Cumulant Matrix Pencil” referenced above, a first order matrix pencil BSS method using a smoothed spatial fourth-order cumulant matrix definition was developed to avoid impractical restrictions on the sensor array characteristics and/or noise environment. The approach therein described exploits the fact that the fourth-order cumulants are insensitive to either spatial or temporal correlation in Gaussian sensor noise since the higher-order cumulants of Gaussian random processes are zero. The method advantageously does not sacrifice any degrees of freedom to estimate a Gaussian noise subspace, making it capable of using all the degrees of freedom for separating as many sources as there are sensors in the array. In order to estimate the adaptive complex sensor weights for separating the multiple sources, a spatial fourth-order cummulant matrix pair is formed for two different sets of time lags between the observations from the different sensors.
A general eigenvalue decomposition of the smoothed Spatial Fourth Order Cumulant Matrix (“SFOCM”) pencil is used to find the adaptive separation weight vectors. Since the generalized eigenvectors are orthogonal to all but one of the steering vectors, the adaptive weights are formed from normalized eigenvectors. These weights maintain gain on a particular source while minimizing the output power due to the other intervening sources. However, the normalized eigenvector weights do not reduce the output power due to additive Gaussian noise at the sensors. Accordingly, an improved blind source separation technique is desired.
Thus embodiments of the disclosed subject matter are extensions and counter parts to the SFOCMP approach, which minimize the output power of the interferers and the output power of the Gaussian sensor noise.
In one embodiment of the present invention, a method for separating a plurality of signals provided by a respective plurality of sources and received by an array comprising a plurality of elements, includes generating a separation matrix as a function of time differences between receipt of the plurality of signals by the plurality of elements, a spatial fourth order cumulant matrix pencil or a pair of 2nd order correlation matrices, a spatial correlation matrix and steering vectors of said plurality of signals. The method also includes multiplying the separation matrix by a matrix representation of the plurality of signals.
In another embodiment of the present invention, a system for separating a plurality of signals provided by a respective plurality of sources includes a receiver for receiving the plurality of signals and for providing received signals. The system also includes a signal processor for receiving the received signals, generating a separation matrix, and multiplying the separation matrix by a matrix representation of the received signals. The separation matrix is a function of time differences between receipt of the plurality of signals by the receiver, a function of a spatial fourth order cumulant matrix pencil or a pair of 2nd order correlation matrices, a spatial correlation matrix and steering vectors of said plurality of signals.